2 questions:

What is it? -1point to each character exhausted at the moment that the treachery is when revealed? or when each character is exhausted in any moment during the round?

If you want to travel, you must 'reveal' one card? So, is this card revealed and added to staging? It it is so, nobody would travel to here, isn't?

Weighted down is a lasting effect, so anytime a character exhaust or ready, he will gain / lose the -1.

Secret entrance is great when you have a high threat moutain, or when you really need to get rid of location. But yeah, not traveling is fine.